Quantum Computing Boosts Rainforest Carbon Credit Portfolios by 31.6 Per Cent

Optimizing carbon credit portfolios represents a substantial challenge for effective climate mitigation, especially within biodiverse regions like the Brazilian Cerrado. Hugo José Ribeiro from the Federal University of Goiás, alongside co-authors, investigate the application of the Approximate Optimization Algorithm (QAOA) with Zero Noise Extrapolation (ZNE) to a complex, multi-objective territorial planning problem. Their research, executed on near-term intermediate-scale quantum hardware, demonstrates that this QAOA+ZNE workflow consistently surpasses classical optimisation methods, achieving a 31.6% improvement in portfolio score with statistically significant results. This work establishes the empirical utility of current noisy intermediate-scale quantum (NISQ) devices, coupled with error mitigation techniques, for identifying nuanced environmental synergies and offering a scalable template for high-precision conservation policies.

They model an 88-variable portfolio optimisation involving carbon sequestration, biodiversity connectivity, and social impact metrics, executed on intermediate-scale IBM Quantum hardware (ibm_torino and ibm_fez).

The results of seven independent hardware runs demonstrate that the QAOA+ZNE workflow consistently outperforms a classical greedy baseline. The quantum method achieves a mean portfolio score of 58.47 ±6.98, corresponding to a 31.6% improvement over the classical heuristic (44.42), with high statistical significance (p = 0.0009) and a large effect size (Cohen’s d = 2.01).

Optimisation modelling for spatially balancing carbon finance and Cerrado biodiversity

Scientists are addressing significant challenges in implementing effective climate mitigation strategies in Brazil due to its scale and ecological diversity. Policies discussed in global climate forums require translation into concrete territorial decisions with measurable impacts, but this translation faces a mathematical barrier in the Cerrado biome.

The Cerrado, spanning roughly 2 million km2, is a global biodiversity hotspot, yet over 50% of its original area has been converted to agriculture and less than 10% of private lands are protected. This necessitates well-designed projects to preserve vegetation and reduce climate impacts, although recent studies indicate only 16% of carbon credits represent actual emission reductions due to measurement difficulties.

Consequently, selecting preservation areas involves a trade-off between financial returns and biodiversity conservation. Ecologically valuable land often has high opportunity costs, marginalizing environmental criteria and exposing investors to greenwashing risks, a concern highlighted in ESG investment reviews.

Poorly optimised portfolios result in inefficient allocations that appear “green” but generate negligible impact, leading to reputational and economic losses. Rigorous portfolio optimisation is therefore crucial to align profit maximisation with native vegetation protection, turning conservation into a strategic asset.

Rather than viewing greenwashing as a regulatory issue, it is framed as an allocation failure, a portfolio-design problem where weak constraints and mis-specified objectives allow low-integrity outcomes. Classical methods often fail to capture the nuances of this multi-objective challenge, which is characterised as an NP-hard knapsack-type problem.

The exponentially growing search space (2n) at scale justifies the transition to frontier computational paradigms and motivates the exploration of metaheuristics and hybrid approaches. Quantum computing has emerged as a promising framework for combinatorial optimisation. The increasing tension between the urgency of conservation and the intractability of resource allocation positions the Quantum Approximate Optimisation Algorithm (QAOA) as a potential operational core for environmental governance.

Introduced by Farhi et al., QAOA is a hybrid variational algorithm that maps classical objective functions to cost functions whose ground states encode optimal solutions. Recent evidence corroborates its efficacy in orchestrating complex multi-objective portfolios, demonstrating robustness when navigating constrained landscapes fundamental to sustainability planning.

QAOA is designed for Noisy Intermediate-Scale Quantum (NISQ) devices, which imposes limitations due to gate noise and decoherence. Comparative experiments show that current NISQ devices are often outperformed by classical methods. To mitigate these limitations, strategies such as expressive shallow architectures and warm-start initialisation have been proposed, alongside error mitigation techniques like zero noise extrapolation (ZNE), which executes circuits under amplified noise to extrapolate outcomes to idealized conditions.

Despite QAOA’s theoretical promise, its application to real environmental problems remains limited, with most studies relying on simulators or simplified instances. The work addresses a formulation of real-world problems with portfolio selection from 88 municipalities in the Cerrado using empirical data on carbon sequestration, biodiversity, and socioeconomic indicators, presenting a reproducible methodology with a complete experimental protocol on publicly accessible IBM Quantum systems (ibm_torino, ibm_fez).

To provide a rigorous basis for the quantum approach, this section details the translation of environmental and economic constraints into a formal mathematical framework suitable for quantum hardware. Carbon credit portfolios refer to structured allocations of emission reduction or carbon sequestration units across multiple jurisdictions or conservation areas.

Public agencies and institutions increasingly optimise portfolios to maximise mitigation impact under budgetary, ecological, and spatial constraints. In the Cerrado biome, this problem translates into selecting combinations of municipalities whose joint implementation of conservation or restoration actions maximizes carbon sequestration while simultaneously preserving biodiversity connectivity and long-term ecosystem resilience.

The effectiveness of mitigation depends not solely on the individual carbon potential of each area, but on the coordinated selection of regions whose spatial and ecological interactions generate synergistic benefits at the landscape scale. This coordination requirement naturally leads to a combinatorial optimisation formulation.

By expressing portfolio allocation as a constrained Quadratic Unconstrained Binary Optimisation (QUBO) problem, the decision process explicitly accounts for both linear contributions (e.g., expected carbon sequestration and socioeconomic indicators) and quadratic interaction terms representing spatial and ecological synergies between municipalities. This formulation ensures that mitigation outcomes emerge from coherent regional strategies rather than independent local decisions, a property critical to translating climate policy targets into effective territorial actions.

The state of Goiás, located in the Central-West region of Brazil, lies almost entirely within the Cerrado biome, recognised as a global biodiversity hotspot. Paradoxically, this region is at the frontier of Brazilian agribusiness expansion, which has continuously advanced through extensive pasturelands and monocultures since the 1970s.

This generates direct tensions between agricultural development and environmental conservation. Consequently, optimising the carbon credit portfolio becomes particularly challenging in this territory. Studies in Goiás watersheds demonstrate the predominance of flat to gently rolling terrains, characterised by deep and highly mechanizable Oxisols, a geomorphological condition that favors both agriculture and extensive livestock farming.

This natural soil aptitude has resulted in massive conversion of native vegetation to pasturelands and annual agriculture, setting up one of the most accelerated land-use change processes in the biome. On the biome-regional scale, the conversion of native forests and savannas to pasture or monoculture has generated measurable climate impacts, including an average temperature increase of approximately +0.9 ◦C and a reduction of about 10% in evapotranspiration.

These alterations compromise not only the regional climate and water availability, but also the stability of the agroecosystems themselves. Given this complex scenario, optimal selection of portfolios for carbon credit projects becomes simultaneously urgent and intricate, requiring optimisation approaches capable of handling multiple conflicting objectives and nonlinear spatial synergies.

The initial pool of 246 municipalities in the state of Goiás was reduced through a two-stage selection process. First, 128 candidates were retained based on environmental suitability for carbon credit projects and the availability of complete and reliable spatial datasets, including MapBiomas, GEDI/LiDAR, PRODES and socioeconomic indicators.

From this set, the final size of the problem was defined as n = 88 by ranking municipalities in descending order according to their normalized carbon sequestration score ci in the interval, which represents the primary optimisation objective. This selection exhibits a natural discontinuity. The 88th rank municipality achieves a normalized carbon score of 0.795, while the 89th rank municipality drops to −0.207 after normalization, corresponding to a gap of approximately one unit in the normalized score. This sharp separation indicates that the top 88 municipalities form a coherent high-potential group, making the cutoff robust to small perturbations.

Quantum workflow significantly enhances multi-objective portfolio optimisation performance

A mean portfolio score of 58.47, accompanied by a standard deviation of 6.98, was achieved through the implementation of the QAOA+ZNE workflow. This result represents a 31.6% improvement when contrasted with a classical greedy baseline, which yielded a score of 44.42. Validation of the methodology’s temporal stability was performed after a 13-day interval, demonstrating consistent performance despite potential hardware calibration drifts.

The study utilised an 88-variable portfolio optimisation, incorporating carbon sequestration, biodiversity connectivity, and social impact metrics, executed on both ibm_torino and ibm_fez quantum hardware. Initial dataset construction involved a two-stage selection process from a pool of 246 municipalities in the state of Goiás, ultimately focusing on a set of 88 municipalities exhibiting high carbon sequestration potential.

The selection of 88 municipalities was determined by a natural discontinuity in normalized carbon sequestration scores, with the 88th ranked municipality achieving a score of 0.795, while the 89th dropped to −0.207 after normalization. This cutoff point was chosen to balance problem expressiveness with the limitations of current Noisy Intermediate-Scale Quantum hardware, as each decision variable requires one physical qubit. Sensitivity analysis using a Greedy heuristic revealed scores of 33.12, 38.36, 44.42, 51.44, and 59.57 for portfolio sizes of 20, 24, 28, 32, and 36, respectively, demonstrating monotonic scaling.

Quantum optimisation delivers enhanced carbon portfolio performance in the Brazilian Cerrado

Researchers have demonstrated a quantum-inspired approach to optimise carbon credit portfolios, achieving substantial improvements over classical methods in a complex environmental planning scenario. A validation run after thirteen days confirmed the stability of the approach despite potential hardware calibration drifts. This work establishes the practical utility of current noisy intermediate-scale quantum devices in environmental science, showing their capacity to identify complex synergies overlooked by conventional optimisation techniques.

The proposed workflow offers a scalable template for developing high-precision environmental conservation policies. The authors acknowledge limitations inherent in the use of current quantum hardware, specifically the challenges associated with scaling to larger and more complex problems. Future research should explore the application of this methodology to different geographical regions and environmental challenges, as well as investigate the potential for integrating additional data sources and constraints into the optimisation model. Further development of error mitigation techniques could also enhance the performance and reliability of the quantum-inspired approach.